4 papers
Unramified Brauer groups of symmetric products and the Brauer-Manin obstructions
Yongqi Liang, Xingyu Liu, Hui Zhang
This article focuses on smooth, projective, and geometrically integral varieties defined over a number field with torsion-free geometric Picard groups. We establish an isom…
Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle
Yongqi Liang, Yufan Liu
On varieties defined over number fields, we consider obstructions to the Hasse principle given by subgroups of their Brauer groups. Given an arbitrary pair of non-zero finite abeli…
Hasse principle violation for algebraic families of del Pezzo surfaces of degree 4 and hyperelliptic curves of genus congruent to 1 modulo 4
Kai Huang, Yongqi Liang
Let g be a positive integer congruent to 1 modulo 4 and K be an arbitrary number field. We construct infinitely many explicit one-parameter algebraic families of degree 4 del Pezzo…
Product of Brauer--Manin obstruction for 0-cycles over number fields and function fields
Diego Izquierdo, Yongqi Liang, Hui Zhang
It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we p…